Experimental study and thermodynamic modeling of cadmium behavior in the PO₄–SO₄–Ca–Cd–H₂O system using the extended Debye–Hückel model

Abstract

Cadmium (Cd) is a highly toxic heavy metal commonly present as an impurity in phosphate rock and is directly transferred to phosphoric acid (PAC) during the leaching process. This study investigates the thermodynamic behavior of cadmium within the PO₄–SO₄–Ca–Cd–H₂O system to better understand its speciation and potential for removal during PAC production. The Debye–Hückel model was employed to predict the thermodynamic saturation indices of minerals capable of incorporating cadmium into their structures, under varying conditions ranging from dilution to saturation and at different temperatures. To validate the model, a comprehensive comparison was conducted between its predictions and experimental macroscopic measurements (pH, density, and conductivity) across the same temperature range. The results show strong agreement, with Root Mean Square Error (RMSE) values of 0.2118 for pH, 0.0507 g/cm³ for density, and 5.572 mS/cm for conductivity, indicating high predictive accuracy. The R² values are also close to 1, confirming an excellent correlation between measured data and model predictions. In addition, the predicted saturation indices for gypsum (SI ≥ 0) show consistent trends across all studied conditions, confirming the robustness of the thermodynamic predictions. However, the model still presents certain limitations, particularly in its ability to predict all cadmium-containing phases observed experimentally.